Comfortable accommodation in May for 2 persons can be found for between €40 and €80 per night. A meal for two that includes a starter, two main meals, salad and a litre carafe of local wine will cost you around €25-35. This can vary widely depending of level of establishment you eat at. A cheap vegetarian dish (pulses or vegetable) will set you back by no more than €5-6 a plate. If you get your breakfast included at the hotel, that is good because breakfast can add another €15 for the two of you per day.
Considering your interests (great food, hiking, beaches, nightlife unimportant) then Naxos should definitely be your other island. (And Naxos has many daily ferry connections with both Santorini and Athens.) Also, Athens needs at least one full day to explore so you should drop any thoughts about Delphi or Nafplio. Also, I would look into flights from Athens to Santorini on your night of arrival. If you could get to Santorini that night (and move your day in Athens to the end of your trip) you’d almost gain an entire day and could spend two nights on Naxos.
Hi! I have fallen in love with the cyklades and have visited Santorini, Ios, Naxos and Folegandros in late june. Folegandros was the best, a fantastic island. We are now thinking about going to Paros the last week in September. Naoussa seem to be a great place. What’s the weather like in late September? Is it still quite warm? I also wonder about the sea conditions. May the sea be rough at that time of the year? I don’t like wavy ferry rides 😨 Thank you for a good sight!

These groups are generally better connected among themselves than with other groups, so you are probably better advised to target them on this basis. As it’s your first time to Greece, you may want the full-on Greek island experience and you could easily fill your five weeks flitting from one island to the other in the Cyclades. You could start in Kea and work your way down to Milos via Kythnos, Serifos and Sifnos then segue to Paros and Naxos. Dip down to Santorini, up to Mykonos and back to Piraeus. The map will also show plenty of other Cyclades islands to pick and choose from such as Ios, Sikinos, Folegandros, Amorgos, Syros, Tinos and Andros – yes! too many choices, but you will find that sticking to one group it will be easier to get between them. Realistically for a period of five weeks you will not want to be doing more than 6-8 islands.